1. Field of the Invention
The present invention relates to a communication system using Low-Density Parity-Check (LDPC) codes. More particularly, the present invention relates to a channel encoding/decoding method and apparatus for generating LDPC codes with various codeword lengths and code rates from an LDPC code given in high-order modulation.
2. Description of the Related Art
In wireless communication systems, link performance significantly decreases due to various noises in the channels, a fading phenomenon, and Inter-Symbol Interference (ISI). Therefore, in order to realize high-speed digital communication systems, which require high data throughput and reliability, such as the next-generation mobile communication, digital broadcasting, and portable Internet, it is important to develop technology for overcoming the channel noises, fading, and ISI. Recently, an intensive study of error-correcting codes has been conducted as a method for increasing communication reliability by efficiently recovering distorted information.
An LDPC code, first introduced by Gallager in 1960s, has lost favor over time due to its implementation complexity which could not be resolved by the technology at that time. However, as the turbo code, which was discovered by Berrou, Glavieux, and Thitimajshima in 1993, exhibits performance levels approximating Shannon's channel limit, research has been conducted on iterative decoding and channel encoding based on a graph along with analyses on performance and characteristics of the turbo code. With this as a momentum, the LDPC code was restudied in the late 1990s, which proved that the LDPC code exhibits performance levels approximating the Shannon's channel limit if the LDPC undergoes decoding by applying iterative decoding based on a sum-product algorithm on a Tanner graph (a special case of a factor graph) corresponding to the LDPC code.
The LDPC code is commonly represented using a graph representation technique, and many characteristics can be analyzed through the methods based on graph theory, algebra, and probability theory. Generally, a graph model of channel codes is useful for description of codes, and by mapping information on encoded bits to vertexes in the graph and mapping relations between the bits to edges in the graph, it is possible to consider the graph as a communication network in which the vertexes exchange predetermined messages through the edges, thus making it possible to derive a natural decoding algorithm. For example, a decoding algorithm derived from a trellis, which can be regarded as a kind of graph, may include the well-known Viterbi algorithm and a Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm.
The LDPC code is generally defined as a parity-check matrix, and can be expressed using a bipartite graph, which is referred to as a Tanner graph. The bipartite graph is a graph where vertexes forming the graph are divided into two different types, and the LDPC code is represented with the bipartite graph consisting of vertexes, some of which are called variable nodes and the other of which are called check nodes. The variable nodes are one-to-one mapped to the encoded bits.
A graph representation method for the LDPC code will be described with reference to FIGS. 1 and 2.
FIG. 1 illustrates an example of a parity-check matrix H1 of an LDPC code with 4 rows and 8 columns. Referring to FIG. 1, because the number of columns is 8, the parity-check matrix H1 signifies an LDPC code that generates a length-8 codeword, and the columns are mapped to 8 encoded bits on a one to one basis.
FIG. 2 illustrates a Tanner graph corresponding to the parity-check matrix H1 in FIG. 1.
Referring to FIG. 2, the Tanner graph of the LDPC code includes 8 variable nodes x1 (202), x2 (204), x3 (206), x4 (208), x5 (210), x6 (212), x7 (214), and x8 (216), and 4 check nodes 218, 220, 222, and 224. An ith column and a jth row in the parity-check matrix H1 of the LDPC code are mapped to a variable node xi and a jth check node, respectively. In addition, a value of 1, i.e. a non-zero value, at the point where an ith column and a jth row in the parity-check matrix H1 of the LDPC code cross each other, indicates that there is an edge between the variable node xi and the jth check node on the Tanner graph as shown in FIG. 2.
In the Tanner graph of the LDPC code, a degree of the variable node and the check node indicates the number of edges connected to each respective node, and the degree is equal to the number of non-zero entries in a column or row corresponding to the pertinent node in the parity-check matrix of the LDPC code. For example, in FIG. 2, degrees of the variable nodes x1 (202), x2 (204), x3 (206), x4 (208), x5 (210), x6 (212), x7 (214), and x8 (216) are 4, 3, 3, 3, 2, 2, 2, and 2, respectively, and degrees of check nodes 218, 220, 222, and 224 are 6, 5, 5, and 5, respectively. In addition, the numbers of non-zero entries in the columns of the parity-check matrix H1 of FIG. 1, which correspond to the variable nodes in FIG. 2, coincide with their degrees 4, 3, 3, 3, 2, 2, 2, and 2, and the numbers of non-zero entries in the rows of the parity-check matrix H1 of FIG. 1, which correspond to the check nodes in FIG. 2, coincide with their degrees 6, 5, 5, and 5.
In order to express degree distribution for the nodes of the LDPC code, a ratio of the number of degree-i variable nodes to the total number of variable nodes is defined as fi, and a ratio of the number of degree-j check nodes to the total number of check nodes is defined as gj. For example, for the LDPC code corresponding to FIGS. 1 and 2, f2=4/8, f3=3/8, f4=1/8, and fi=0 for i≠2, 3, 4; and g5=3/4, g6=1/4, and gj=0 for j≠5, 6. When a length of the LDPC code, i.e. the number of columns, is defined as N, and the number of rows is defined as N/2, the density of non-zero entries in the entire parity-check matrix having the above degree distribution is computed as shown in Equation (1).
                                                        2              ⁢                              f                2                            ⁢              N                        +                          3              ⁢                              f                3                            ⁢              N                        +                          4              ⁢                              f                4                            ⁢              N                                            N            ·                          N              /              2                                      =                  5.25          N                                    (        1        )            
In Equation (1), as N increases, the density of 1's in the parity-check matrix decreases. Generally, as for the LDPC code, because the codeword length N is inversely proportional to the density of non-zero entries, the LDPC code with a large N has a very low density of non-zero entries. The term “low-density” in the name of the LDPC code originates from the above-mentioned relationship.
Next, with reference to FIG. 3, a description will be made of characteristics of a parity-check matrix of a structured LDPC code applicable to the present invention. FIG. 3 illustrates an LDPC code adopted as the standard technology in Digital Video Broadcasting-Satellite transmission 2nd generation (DVB-S2), which is one of the European digital broadcasting standards.
In FIG. 3, N1 and K1 denote a codeword length and an information length (or a length of an information word) of an LDPC code, respectively, and (N1−K1) provides a parity length. Further, integers M1 and q are determined to satisfy q=(N1−K1)/M1. Preferably, K1/M1 should also be an integer. The parity-check matrix in FIG. 3 will be referred to herein as a first parity-check matrix H1, for convenience only.
Referring to FIG. 3, a structure of a parity part, i.e. K1th column through (N1−1)th column, in the parity-check matrix, has a dual diagonal shape. Therefore, as for degree distribution over columns corresponding to the parity part, all columns have a degree ‘2’, except for the last column having a degree ‘1’.
In the parity-check matrix, a structure of an information part, i.e. 0th column through (K1−1)th column, is made using the following rules.
Rule 1: A total of K1/M1 column groups are generated by grouping K1 columns corresponding to the information word in the parity-check matrix into multiple groups each including M1 columns. A method for forming columns belonging to each column group follows Rule 2 below.
Rule 2: First, positions of ‘1’s in each 0th column in ith column groups (where i=1, . . . , K1/M1) are determined. When a degree of a 0th column in each ith column group is denoted by Di, if positions of rows with 1 are assumed to be Ri,0(1), Ri,0(2), . . . , Ri,0(Di), positions Ri,j(k) (k=1, 2, . . . , Di) of rows with 1 are defined as shown in Equation (2), in a jth row (where j=1, 2, . . . , M1−1) in an ith column group.Ri,j(k)=Ri,(j−1)(k)+q mod(N1−K1),  (2)                k=1, 2, . . . , Di, i=1, . . . , K1/M1, j=1, . . . , M1−1        
According to the above rules, it can be appreciated that degrees of columns belonging to an ith column group are all equal to Di. For a better understanding of a structure of a DVB-S2 LDPC code that stores information on the parity-check matrix according to the above rules, the following detailed example will be described.
As a detailed example, for N1=30, K1=15, M1=5, and q=3, three sequences for information on the positions of rows with 1 for 0th columns in 3 column groups can be expressed as follows. Herein, these sequences are called “weight-1 position sequences.”R1,0(1)=0, R1,0(2)=1, R1,0(3)=2,R2,0(1)=0, R2,0(2)=11, R2,0(3)=13,R3,0(1)=0, R3,0(2)=10, R3,0(3)=14.
Regarding the weight-1 position sequence for 0th columns in each column group, only the corresponding position sequences can be expressed as follows for each column group. For example:
0 1 2
0 11 13
0 10 14.
In other words, the ith weight-1 position sequence in the ith line sequentially represents information on the positions of rows with 1 in the ith column group.
It is possible to generate an LDPC code having the same concept as that of a DVB-S2 LDPC code in FIG. 4, by forming a parity-check matrix using the information corresponding to the detailed example, and Rules 1 and 2.
It is known that the DVB-S2 LDPC code designed in accordance with Rules 1 and 2 can be efficiently encoded using the structural shape. Respective steps in a process of performing LDPC encoding using the DVB-S2 based parity-check matrix will be described below by way of example.
In the following description, as a detailed example, a DVB-S2 LDPC code with N1=16200, K1=10800, M1=360, and q=15 undergoes an encoding process. For convenience, information bits having a length K1 are represented as (i0, i1, . . . , iK1−1), and parity bits having a length (N1−K1) are expressed as (p0, p1, . . . , pN1−K1−1).
Step 1: An LDPC encoder initializes parity bits as follows:p0=p1= . . . =pN1−K1−1=0
Step 2: The LDPC encoder reads information on rows where 1 is located in a column group from a 0th weight-1 position sequence out of the stored sequences indicating the parity-check matrix.
0 2084 1613 1548 1286 1460 3196 4297 2481 3369 3451 4620 2622R1,0(1)=0, R1,0(2)=2048, R1,0(3)=1613, R1,0(4)=1548, R1,0(5)=1286,R1,0(6)=1460, R1,0(7)=3196, R1,0(8)=4297, R1,0(9)=2481, R1,0(10)=3369,R1,0(11)=3451, R1,0(12)=4620, R1,0(13)=2622.
The LDPC encoder updates particular parity bits px in accordance with Equation (3), using the read information and the first information bit i0. Herein, x is a value of R1,0(k) for k=1, 2, . . . , 13.p0=p0⊕i0, p2084=p2064⊕i0, p1613=p1613⊕i0,p1548=p1548⊕i0, p1286=p1286⊕i0, p1460=p1460⊕i0,p3196=p3196⊕i0, p4297=p4297⊕i0, p2481=p2481i⊕i0,p3369=p3369⊕i0, p3451=p3451⊕i0, p4620=p4620⊕i0,p2622=p2622⊕i0  (3)
In Equation (3), px=px ⊕ i0 can also be expressed as px←px ⊕ i0, and ⊕ represents binary addition.
Step 3: The LDPC encoder first determines a value of Equation (4) for the next 359 information bits im (where m=1, 2, . . . , 359) after i0.{x+(m mod M1)×q} mod(N1−K1), M1=360, m=1,2, . . . ,359  (4)
In Equation (4), x is a value of R1,0(k) for k=1, 2, . . . , 13. It should be noted that Equation (4) is similar to Equation (2).
Next, the LDPC encoder performs an operation similar to Equation (3) using the values found in Equation (4). In other words, the LDPC encoder updates parity bits p{x+(m mod M1)×q} mod(N1−K1) for im. For example, for m=1, i.e. for i1, the LDPC encoder updates parity bits p(x+q)mod(N1−K1) as defined in Equation (5).p15=p15⊕i1, p2099=p2099⊕i1, p1628=p1628⊕i1,p1563=p1563⊕i1, p1301=p1301⊕i1, p1475=p1475⊕i1,p3211=p3211⊕i1, p4312=p4312⊕i1, p2496=p2496⊕i1,p3384=p3384⊕i1, p3466=p3466⊕i1, p4635=p4635⊕i1,p2637=p2637⊕i1  (5)
It is to be noted that q=15 in Equation (5). The LDPC encoder performs the above process for m=1, 2, . . . , 359, in the same manner as shown above.
Step 4: As in Step 2, the LDPC encoder reads information of the 1st weight-1 position sequence R2,0(k) (k=1, 2, . . . , 13) for a 361st information bit i360, and updates particular parity bits px, where x is R2,0(k). The LDPC encoder updates p{x+(m mod M1)×q} mod(N1−K1), m=361, 362, . . . , 719 by similarly applying Equation (4) to the next 359 information bits i361, i362, . . . , i719 after i360.
Step 5: The LDPC encoder repeats Steps 2, 3, and 4 for all groups each having 360 information bits.
Step 6: The LDPC encoder finally determines parity bits using Equation (6).pi=pi⊕pi−1, i=1,2, . . . , N1−K1−1  (6)
The parity bits pi of Equation (6) are parity bits that have completely undergone LDPC encoding.
As described above, DVB-S2 carries out encoding through the process of Steps 1 to 6.
In order to apply the LDPC code to the actual communication system, the LDPC code should be designed to be suitable for the data rate required in the communication system. Particularly, not only in an adaptive communication system employing Hybrid Automatic Retransmission reQuest (HARQ) and Adaptive Modulation and Coding (AMC), but also in a communication system supporting various broadcast services, LDPC codes having various codeword lengths are needed to support various data rates according to the system requirements.
However, as described above, the LDPC code used in the DVB-S2 system has only two types of codeword lengths due to its limited use, and each type of the LDPC code needs an independent parity-check matrix. For these reasons, there is a long-felt need in the art for a method for supporting various codeword lengths to increase extendibility and flexibility of the system. Particularly, in the DVB-S2 system, transmission of data having several hundreds to thousands of bits is needed for transmission of signaling information. However, because only 16200 and 64800 are available for lengths of the DVB-S2 LDPC code, there is a still a need for support of various codeword lengths. Yet, since storing independent parity-check matrixes for respective codeword lengths of the LDPC code may reduce memory efficiency, there is a need for a scheme capable of efficiently supporting various codeword lengths from the given existing parity-check matrix, without designing a new parity-check matrix.